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Proof step 289 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf), m4 < EB_PAGE_SIZE, m2 < # avol1, abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ LEB_SIZE, m0 ≤ m6 + m4, m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, # buf ≤ LEB_SIZE, m6 ≤ # buf, (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ # buf3, ¬ m0 ≤ m6 → m6 ≤ m0, ¬ rofs → # buf = m6 ⊦ (m0 ≤ m6 ⊃ 0;m0 - m6) ≤ m4 ∧ (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ EB_PAGE_SIZE

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 290:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf, avol0[m2] = mapped(buf), avol1[m2] = mapped(buf1), m2 < # avol1, m4 < EB_PAGE_SIZE, abs(avol1, buffered(m2), mkwbuf(buf2, m6, m4), avol0, rofs), awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), (m0 ≤ m6 ⊃ m6 - m0;0) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ # buf3, m6 ≤ # buf, # buf ≤ LEB_SIZE, m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ LEB_SIZE, n1 + (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, m6 ≤ m0 + n1 + (m0 ≤ m6 ⊃ m6 - m0;0), m0 ≤ m6 + m4, m6 ≤ LEB_SIZE, (m0 ≤ m6 ⊃ m6 - m0;0) ≤ # buf3, ¬ rofs → # buf = m6, ¬ m0 ≤ m6 → m6 ≤ m0 ⊦ m0 ≤ m6, (m0 ≤ m6 ⊃ 0;m0 - m6) ≤ m4 ∧ (m0 ≤ m6 ⊃ 0;m0 - m6) + min(n1, m4 - (m0 ≤ m6 ⊃ 0;m0 - m6)) ≤ EB_PAGE_SIZE

Rule argument

fma: m0 ≤ m6

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ m - 0 = m; (s)% ⊦ 0 ≤ m; (s)% ⊦ n + 0 = n; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ ¬ m < min(n, m); (s) Used formulas: m0 ≤ m6